{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:AEBIKQSQ2JQH325E5NNPW7ORX6","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d2678564957fa967ba76d9d1250c52efa58cd82761bb7206cbdee564d74be3e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-08-17T00:47:39Z","title_canon_sha256":"1237be0095fe384c0411f88535b38998b0dcc1328d37ff33bcaa44b2c90e68f1"},"schema_version":"1.0","source":{"id":"1408.3781","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.3781","created_at":"2026-05-18T02:29:53Z"},{"alias_kind":"arxiv_version","alias_value":"1408.3781v2","created_at":"2026-05-18T02:29:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.3781","created_at":"2026-05-18T02:29:53Z"},{"alias_kind":"pith_short_12","alias_value":"AEBIKQSQ2JQH","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AEBIKQSQ2JQH325E","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AEBIKQSQ","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:436b19355d47451622684d0de8db0692314b0d125ef8e893d8c23545de6bef39","target":"graph","created_at":"2026-05-18T02:29:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We give a constructive proof of the Carath\\'eodory Theorem by means of the concept of a modulus of local connectivity and the extremal distance of the separating curves of an annulus.","authors_text":"Timothy H. McNicholl","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-08-17T00:47:39Z","title":"Carath\\'eodory's Theorem and moduli of local connectivity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3781","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2c1ff4f7b060ce0db8fc4abcb8a8cfdf3acd219288750c4701a25988c5ce24fb","target":"record","created_at":"2026-05-18T02:29:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d2678564957fa967ba76d9d1250c52efa58cd82761bb7206cbdee564d74be3e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-08-17T00:47:39Z","title_canon_sha256":"1237be0095fe384c0411f88535b38998b0dcc1328d37ff33bcaa44b2c90e68f1"},"schema_version":"1.0","source":{"id":"1408.3781","kind":"arxiv","version":2}},"canonical_sha256":"0102854250d2607deba4eb5afb7dd1bf856c13ecdd33bb9b886f492546d28563","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0102854250d2607deba4eb5afb7dd1bf856c13ecdd33bb9b886f492546d28563","first_computed_at":"2026-05-18T02:29:53.635308Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:53.635308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9oEwKT9Lqm34DHt50rkxfvPaJOdbbt39zh/Teppiw5EB5cr03EjBIJi+2ysmPB9akgp02yGyXpwvXM3L3cHYAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:53.635968Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.3781","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c1ff4f7b060ce0db8fc4abcb8a8cfdf3acd219288750c4701a25988c5ce24fb","sha256:436b19355d47451622684d0de8db0692314b0d125ef8e893d8c23545de6bef39"],"state_sha256":"a88e7acae4726fb0a4615efe5da20c508dbf246614ee48936ff91b58ca23807c"}